# Exponential Distribution PDF: Why multiply by lambda?

Hoping you can help me understand the probability density function for the exponential distribution.

Given that the distribution's PDF is described as follows when x > 0:

$$\lambda e^{-\lambda x}$$

Why do we multiply by λ? Sure I'm missing something basic here, but seems that if we're modeling time to event, using e and the exponents would be enough. Is it because we might expect the event to happen multiple times in the time interval?